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arXiv:2304.10480 · Lecture notes in computer science

Secure Computation with Shared EPR Pairs (Or: How to Teleport in Zero-Knowledge)

James Bartusek, Dakshita Khurana, Akshayaram Srinivasan

Published Jan 1, 2023• 3 citations
arXivHTMLPDF
DOI
10.1007/978-3-031-38554-4_8

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Quantum teleportation (QT) provides a useful way to securely transfer unknown quantum state between distant nodes without physically sending the states themselves. In this paper, we present a teleportation scheme of the most general hybrid multi-qudit state via EPR pairs with different dimensions in the chain network. In this structure, the EPR channels shared between neighbor nodes could be distinct, which means that the shared EPR pairs could be different in dimension and the parameters with each other, demonstrating a universality scenario in realistic transmission. In addition, we discuss the condition that can ensure the integrity of the transmitted information with available channel resource, and our scheme could provide a method to solve the resemble problem in the construction of future quantum network.
This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of non-interactive quantum perfect and statistical zero-knowledge. It is also shown that, with sharing EPR pairs a priori, the class of languages having one-sided bounded error non-interactive quantum perfect zero-knowledge proof systems has a natural complete problem. Non-triviality of such a proof system is based on the fact proved in this paper that the Graph Non-Automorphism problem, which is not known in BQP, can be reduced to our complete problem. Our results may be the first non-trivial quantum zero-knowledge proofs secure even against dishonest quantum verifiers, since our protocols are non-interactive, and thus the zero-knowledge property does not depend on whether the verifier in the protocol is honest or not. A restricted version of our complete problem derives a natural complete problem for BQP.
Classical secret sharing proposed by Shamir used classical computational power in classical cryptography to achieve secret key sharing, but with the advent of quantum systems, computational power can be overruled. To ensure a secure secret sharing scheme independent of computational power, a scheme independent of computational complexity is needed to achieve security. This paper will provide a protocol dependent on inherent secure nature of quantum cryptography (quantum no cloning theorem and quantum measurement rule). A secure multiparty quantum secret sharing scheme has been proposed to ensure that no one can eavesdrop or extract any share of the secret message via inherent security provided by quantum entanglement swapping and quantum teleportation. Entanglement swapping is a process that allows two non-interacting quantum systems to be entangled. Whereas, Quantum teleportation allows a party to send a qubit to another entangled party without sending the qubit over the channel. Moreover, in order to ensure security against possible active attacks, sender himself will generate and distribute EPR pairs to be used in the scheme. Result will be a secure multiparty QSS scheme which will be secure against internal and external eavesdropping, masquerading and brute-force attacks.